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On Montgomery's conjecture and the distribution of Dirichlet sums |
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| Authors: | Per H Enflo Vladimir I Gurariy Juan B Seoane-Sepúlveda |
| Institution: | 1. Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;2. Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain |
| Abstract: | A new version of Montgomery's conjecture (1971) on the estimation of Dirichlet sums is disproved by means of a modification of the idea of “short sums” (due to Bourgain, 1991). We also study the distribution of the values of Dirichlet's “long sums”. |
| Keywords: | 11M99 11M26 |
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